Passage III

Maryam Mirzakhani's Abstractions

Maryam Mirzakhani believes the beauty of mathematics only shows itself to patient followers. Few have followed math more patiently than she has. In 2014, at age thirty-seven, Iranian-born Mirzakhani became the first woman, to win the Fields Medal math's most prestigious prize. Her research focus, highly abstract, theoretical problems relating to geometry, is so imaginative and astonishingly complex that they defy explanation even to many practiced mathematicians.

Mirzakhani's thinking about her mathematical research is as imaginative as the problems she challenges herself to solve. She compares her work to that of a writer crafting a novel. To her, math research is a slow, steady process of watching characters evolve.

Mirzakhani studies the geometry of curved surfaces. Her characters are spheres, doughnut-shaped objects, and wavering planes. Monotonous, playful drawings of these curved forms, interspersed with equations and mathematical notes, cover huge sheets of white paper spread out over her office floor. While her young daughter, Anahita, often watches on, Mirzakhani can visualize that her first impression of a character was wrong or that two seemingly opposing characters are connected. Like a writer who believes strong characters will act with accord to their natures as a story unfolds, Mirzakhani tries not to predict what connections her shapes and equations will make next. This approach has helped her find solutions so clear and elegant that her colleagues refer to this as profound events in math.

Over several years, she felt optimistic as she got to know her characters better, finally seeing them clearly.

Secondly, a few particularly labyrinthine plots have played out before Mirzakhani for over a decade. In 2014, researchers across the discipline has been wondering what new mathematical tales the Stanford professor and Fields medalist would conceptualize next. And what beautiful solutions she would slowly find.